"This is not only a responsible, reasonable, balanced plan," Ryan said, "it's also an invitation. This is an invitation to the president of the United States, to the Senate Democrats to come together to fix these problems."

But just as Obama has made new overtures to Ryan and other Capitol Hill Republicans in hopes of breaking the fiscal logjam in Congress, Ryan produced a new budget that offers up few concessions to Democrats, and doubles down upon many of the policies on which Republicans campaigned during last fall's election.

The new Ryan budget calls for repealing Obama's signature health care reform law, and sweeping changes to Medicare for anyone under the age of 54 — familiar policies for which Republicans have aggressively pushed during the last two years.

The budget's goal would be to eliminate all but two income tax brackets, one at 10 percent and the other at 25 percent; it would raise no new revenue through taxes, cutting against the president's own demands for additional revenue.

"While the House Republican budget aims to reduce the deficit, the math just doesn't add up," White House press secretary Jay Carney said in a statement.

But the White House stopped short of waging a blistering assault on the Ryan plan, offering a glimmer of hope that bipartisanship might still eventually carry the day.

"While the president disagrees with the House Republican approach, we all agree we need to leave a better future for our children," Carney said. "The president will continue to work with Republicans and Democrats in Congress to grow the economy and cut the deficit in a balanced way."

Getty Images

Still, Ryan defended the generally unflinching conservatism of his budget.

"That means we surrender our principles? That means we stop believing in what we believe in?" he asked at a press conference to debut his proposals. "Elections do have consequences ... This is our offer, this is our vision."

The GOP proposal comes amid new overtures by Obama to Republicans in Congress. The president had lunch last week with Ryan, and dinner with a group of GOP senators.

Obama will address House and Senate Republicans separately this week, marking a pivot in his strategy toward vexing fiscal issues following bruising battles over the fiscal cliff during the first two months of this year.

CNBC's John Harwod reports the White House has rejected Rep. Ryan's budget proposal that included $4.6 trillion in budget cuts but included no new revenues.

This latest GOP plan — the third authored by Ryan since Republicans retook the House in 2010 — is the opening salvo in a spring full of budget battles, culminating in the mid-May expiration of the nation's borrowing authority. Congress authorized a suspension of the debt limit through that deadline, but made it contingent upon the House and Senate each passing their own budget. (Republicans have repeatedly needled Senate Democrats for failing to pass a budget in recent years.)

"I hate to break the suspense, but their budget won't balance—ever," Ryan wrote in an op-ed for the Wall Street Journal. "We House Republicans have done our part … Now we invite the president and Senate Democrats to join in the effort."

Ryan's blueprint claims to achieve $4.6 trillion in savings over through 2023, and steadily reduce government spending as a share of gross domestic product in the meantime. In his op-ed, Ryan asserted the reforms could boost gross national product by as much as 1.7 percent. Ryan's previous plan projected a balanced budget outside of ten years.

But the plan also relies on savings accrued from two plans which Republicans had staunchly opposed: the new taxes on the wealthy in the Jan. 1 fiscal cliff deal, and the $715 billion in savings from cuts to Medicare providers as part of Obama's health care reform law.

Of the new taxes, Ryan said that Republicans were "not going to re-fight the past." When pressed as to how that principle squares with his budget's goal of repealing Obamacare, Ryan pivoted, and said that the health reform law would be so onerous, that the eventual GOP replacement would be an improvement.

It would achieve its goal through a series of sweeping reforms, most of which are unlikely to survive the Democratic Senate or a presidential veto threat.

Ryan's budget again seeks changes to Medicare, namely by establishing an exchange of private plans (including traditional Medicare) from which seniors could choose, with the assistance of a premium support voucher. The plan would apply for those under the age of 54 — a threshold one year younger than past Ryan proposals — and also employ means-testing, in which wealthier seniors pay a higher share of their premiums.

The Ryan budget also calls for repealing the health care reform law (though it would leave in place savings from cuts in payments to medical providers, a component against which Ryan and Mitt Romney railed during last fall's campaign).

The campaign also focused heavily on Ryan's past budgets, as Obama and Democratic candidates downballot railed against similar proposed changes to entitlement programs. Those attacks offered a vivid illustration of the political difficulties in putting such aggressive reform plans to paper. That experience helped inform the GOP's demand that Democrats produce their own alternative budget, through which Republican staffers will surely comb to exploit politically.

Ryan's own budget isn't short on additional conservative prescriptions, either. The 2014 budget calls for sweeping tax reform, with a goal of cutting the top corporate tax rate to 25 percent, and simplifying the income tax into two brackets. The tax cuts would be financed by closing loopholes and deductions in the tax code.

The Republican budget will also touch upon other social programs. It would block-grant Medicaid to states, and allow states more flexibility, too, in implementing welfare programs. Ryan's plan would also freeze the current maximum support for students awarded as Pell Grants, a popular program with students (and young voters) that Obama had expanded in his first term.

The proposals, as a whole, amount to a deeply conservative set of proposals offered against the backdrop of new hopes for bipartisan fiscal talks in Washington.

Obama's renewed outreach — and Republicans' relatively warm reception of it — has stoked the embers of hope that lawmakers may finally reach the kind of grand fiscal deal that has eluded them during the past few years. As Ryan unveils his new budget, Obama's own reaction could either preserve these renewed hopes, or allow them to wither after just a few days.

To that end, Obama was set to speak to House Republicans on Wednesday, and Senate Republicans on Thursday. He was also scheduled to give an interview to ABC News on Tuesday, which could be his first on-camera reactions to Ryan's new proposal.